Question

Which of the following gives the remainder on dividing \[ x^{3}-2 x^{2}-12 x+c \] by \[ x^{2}+3 x+3 \text {, } \] where \( \boldsymbol{c} \) is a real number? \( c+12 \) \( c+15 \) \( x-5 \) \( -5 x^{2}-15 x+c \) \( x^{3}-6 x+c+6 \)

          Which of the following gives the remainder on dividing
\[
x^{3}-2 x^{2}-12 x+c
\]
by
\[
x^{2}+3 x+3 \text {, }
\]
where \( \boldsymbol{c} \) is a real number?
\( c+12 \)
\( c+15 \)
\( x-5 \)
\( -5 x^{2}-15 x+c \)
\( x^{3}-6 x+c+6 \)

Which of the following gives the remainder on dividing

x^3-2 x^2-12 x+c

by

x^2+3 x+3 ,

where c is a real number?
c+12
c+15
x-5
-5 x^2-15 x+c
x^3-6 x+c+6

Added by Adam L.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Yujie Wang

Step 1

We need to find the remainder when the polynomial \( x^3 - 2x^2 - 12x + c \) is divided by \( x^2 + 3x + 3 \). The remainder, when a polynomial \( f(x) \) is divided by another polynomial \( g(x) \) where the degree of \( g(x) \) is less than or equal to the Show more…

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Which of the following gives the remainder on dividing \[ x^{3}-2 x^{2}-12 x+c \] by \[ x^{2}+3 x+3 \text {, } \] where \( \boldsymbol{c} \) is a real number? \( c+12 \) \( c+15 \) \( x-5 \) \( -5 x^{2}-15 x+c \) \( x^{3}-6 x+c+6 \)